Math Review of Exponents Solution Key

Review of Exponents [Day 6] Name: Key COMPOUNDING INTEREST Annually n = 1 Weekly n = 52 Monthly n = 12 Quarterly n = 4 Daily n = 365 Hourly n = 8760 A = P(1 + r/n)^(nt) A = Pe^(rt) Continuously Use a calculator to evaluate in #1-#8. 1. e^(0.08) = 1.083 2. e^(2.1) = 8.166 3. e^(-4) = 0.018 4. e^(1.3) = 3.67 5. e¹ = 2.718 6. e⁰ = 1 7. e^(1/2) = 1.649 8. Which is larger, e^π or π^e? e^π = 23.141 π^e = 22.459 e^π 9. Suppose you invest $500 at 5% annual interest. Calculate the amount you would have after one year if the interest is compounded as follows: P = 500, r = 0.06, t = 1 a. quarterly: 500(1 + 0.06/4)^(4*1) = $530.68 b. monthly: 500(1 + 0.06/12)^(12*1) = $530.84 c. daily: 500(1 + 0.06/365)^(365*1) = $530.92 d. continuously: 500e^(0.06*1) = $530.92 Define: Effective Annual Yield percent increase! New-original original 10. Find the effective annual yield for each answer in #9. a. 530.68-500 500 =6.136% b. 530.84-500 500 =6.168% 53092-500 500 6.184% d. 530.92-500 500 = 6.184% e. Why are these four answers greater than the original interest rate in #9? Answers will vary: these are the actual rates that were applied based on the unit for compounding. This is what was actually earned. 11. One hundred dollars deposited in a bank that compounds interest quarterly yields $107.50 over 1 year. a. Find the annual interest rate b. Find the effective annual yield 107.50=100(1+)(1) 4/1075=1+ 1.075=(1+5) 47.075-1=4:42.035-1] 107.50-100 100 0.075 7.5% 12. After a year during which interest is compounded quarterly, an investment of $800 is worth $851. What is the effective annual yield? 851-800 800 = 6.375% 13. With which plan would an investor earn more, Plan A or Plan B Plan A Plan A: A 6% annual rate compounded annually over a 10-year period 10 1(1+00) = 1.7908 Plan B: A 5.5% annual rate compounded quarterly over a a 10-year period 1(1+-0554 4)=1.7268 14. With which plan would an investor earn more, Plan A or Plan B Plan A: Plan A A 8% annual rate compounded quarterly over a 5-year period 1(1+-08)4(5)= 4) 1.4859 Plan B: A 7.5% annual rate compounded daily over a 5-year period 1(1+045345(5) : 1.4549 15. Suppose that $1000 is invested at 7% interest compounded continuously. How much money would be in the bank after 5 years? 10000.07(5) $1419.07 Define: Rule of 72 16. Suppose that $1000 is invested at 8% interest compounded annually. How long would it take for the investment to double? 72 9 years 17. Suppose that $2050 is invested at 6% interest compounded monthly. How long would it take for the investment to double? 7212 years 18. Suppose that $3200 is invested at 2.5% interest compounded monthly. How long would it take for the investment to double? 72 2.5 28.8 years